Answer
$s\in\{ \displaystyle \frac{\pi}{4}$ , $\displaystyle \frac{3\pi}{4},\ \displaystyle \frac{5\pi}{4},\ \displaystyle \frac{7\pi}{4} \}$
Work Step by Step
For any real number $s$ represented by a directed arc on the unit circle,
$\sin s=y\quad \cos s=x \quad \displaystyle \tan s=\frac{y}{x} (x\neq 0)$
Use Figure 13 on page 111.
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In the interval $[0,2\pi)$, (the unit circle), we search for
points (x,y), such that $x^{2}=\displaystyle \frac{1}{2}$
$(\cos s=x)$
$x^{2}=\displaystyle \frac{1}{2}\qquad /\sqrt{...}$
$x=\displaystyle \pm\sqrt{\frac{1}{2}}=\pm\frac{1}{\sqrt{2}}\cdot\frac{\sqrt{2}}{\sqrt{2}}=\pm\frac{\sqrt{2}}{2}$
We find 4 such points (with x-coordinates of $\displaystyle \pm\frac{\sqrt{2}}{2}),$
assigned to radian measures
$\displaystyle \frac{\pi}{4}$ , $\displaystyle \frac{3\pi}{4},\ \displaystyle \frac{5\pi}{4},\ \displaystyle \frac{7\pi}{4}$ (see image below)
$s\in\{ \displaystyle \frac{\pi}{4}$ , $\displaystyle \frac{3\pi}{4},\ \displaystyle \frac{5\pi}{4},\ \displaystyle \frac{7\pi}{4} \}$
